Best Known (149, 149+∞, s)-Nets in Base 4
(149, 149+∞, 130)-Net over F4 — Constructive and digital
Digital (149, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (149, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(149, 149+∞, 215)-Net over F4 — Digital
Digital (149, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (149, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(149, 149+∞, 464)-Net in Base 4 — Upper bound on s
There is no (149, m, 465)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (149, 2319, 465)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42319, 465, S4, 5, 2170), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 52 263640 435229 196547 619221 464016 346398 247599 966288 516897 690322 907273 492865 714899 883358 750546 817195 324468 013027 483454 813573 680405 562097 428723 041688 709044 107324 809686 379008 444889 550185 517796 811909 261335 621874 452214 089182 480501 730741 983284 141318 867123 452245 716778 633095 869515 613392 371627 352693 661729 320847 914589 576407 688713 225857 267342 904139 810021 304686 216993 136273 289657 191459 894100 277163 787521 121632 641554 555146 284295 516886 274862 194647 689278 533490 982919 933450 297717 249979 800858 024188 770187 353327 230196 843082 377548 908074 456006 101263 364278 803675 050334 930540 687943 592036 858499 234347 018877 462253 168235 487287 619234 823149 810835 373390 607089 752275 394394 936439 446880 946962 639129 638827 858783 971818 793824 009465 613814 686217 935584 708274 433746 694933 603881 990151 382233 836599 175616 363192 849870 939512 776279 012802 411420 624451 043572 568256 652067 779831 182904 692430 220293 857896 971183 265017 019713 040206 686107 312402 652962 924544 615319 079123 160985 064796 335190 733596 844722 741848 902671 561200 612176 931983 869541 639692 124101 246812 729016 736720 224493 251635 965293 906988 502447 354943 162257 835181 834130 852323 797663 389965 513057 095960 539607 077172 381566 291865 292550 441715 671344 057415 162414 968822 847399 079236 300380 202599 946089 963378 493078 367336 335131 114215 193809 073758 339002 863626 868667 421645 569086 472645 547224 477814 658493 127805 567655 869173 262690 749632 554585 150253 158332 926913 033237 293764 118171 346233 252869 022363 103751 224627 090821 759939 641344 / 2171 > 42319 [i]
- extracting embedded OOA [i] would yield OOA(42319, 465, S4, 5, 2170), but